Quadrature-phase signals I/Q have been commonly applied to wireless transceivers. It can be realized by either a quadrature down-conversion mixer or a polyphase filter. In a non-zero-IF receiver architecture, I/Q signals are essential for post frequency conversion image rejection, while in a zero-IF receiver architecture, I/Q signals are required for non-coherent demodulation. Please refer to FIG. 1, in which a block diagram of a typical radio receiver is illustrated. After a radio-frequency signal RF is received via an antenna 10, the signal RF is demodulated into an in-phase signal I and a quadrature-phase signal Q by multiplying sin(ωt) and cos(ωt), respectively. The quadrature-phase signal Q, after being phase-delayed by 90 degrees, is added to the in-phase signal I so as to obtain an image-free intermediate frequency signal IF.
Various analog image cancellation structures have been introduced, such as Weaver image rejection mixer, Hartley image rejection mixer, and complex filter. Ideally, the gains and phases of the in-phase signal I and the quadrature-phase signal Q are conformable to each other. In other words, the amplitudes of the in-phase signal I and the quadrature-phase signal Q are supposed to be the same, and the phase difference between the in-phase signal I and the quadrature-phase signal Q is supposed to be 90 degrees so that the image is completely rejected. In practice, however, a perfect balance between the in-phase signal I and quadrature-phase signal Q does not occur. There is generally difference existing between the amplitudes of the in-phase signal I and the quadrature-phase signal Q, and the phase difference between the in-phase signal I and quadrature-phase signal Q is hardly kept at perfectly 90 degrees. As the conventional circuits mentioned above are highly sensitive to the possible imbalance between the in-phase signal I and the quadrature-phase signal Q, the achievable rejection ratio has been limited 30 to 35 dB. The following equation describes the relation between an image rejection ratio (IRR) and gain/phase mismatches of I/Q signals:
      IRR    ⁡          (      dB      )        =            -      10        ⁢          log      (                                                  (                              Δ                ⁢                                                                  ⁢                                  A                  /                  A                                            )                        2                    +                      θ            2                          4            )      where ΔA/A is defined as relative gain mismatch and θ is the phase mismatch. The result is plotted in FIG. 2.
In many radio receivers, a 30-dB IRR is insufficient to fulfill the system performance requirement. For example, a 60-dB IRR is required for terrestrial TV receiver due to a conceivable scenario that the image channel interference can be 40 dB higher than the desired channel signal. From FIG. 2, it is seen that to attain 60 dB IRR, the gain and phase mismatch must be kept below 0.01 dB and 0.1 degree, respectively, which is unlikely to be achieved repetitively in analog domain without any calibration circuits.
In consequence, several correction techniques have been developed for compensating the imbalance, which are listed below and incorporated herein for reference:    [1] L. Der and B. Razavi, “A 2 GHz CMOS Image-Rejection Receiver with LMS Calibration,” IEEE J. of Solid-State Circuits, Vol. 38, pp. 167-175, February 2003;    [2] C. Heng et. al., “A CMOS TV Tuner/Demodulator IC with Digital Image Rejection,” IEEE J. OF Solid-State Circuits, Vol. 40, No. 12, pp. 2525-2535, December 2005;    [3] S. Lerstaveesin and B. Song, “A Complex Image Rejection Circuit with Sign Detection Only,” ISSCC Technical Digest, Session 25.2, 2006;    [4] M. Hajirostam and K. Martin, “On-chip Image Rejection in a Low-IF CMOS Receiver,” ISSCC Technical Digest, Session 25.3, 2006;    [5] G. M. Desjardins, “Adaptive Digital Signal Processing Algorithms for Image-Rejection Mixer Self-Calibration,” UC Berkeley MS. Thesis, 2000; and    [6] I. Sever, “Adaptive Calibration Methods for an Image Rejection Mixer,” UC Berkeley MS. Thesis, 2002.